Star-multiplicative graphs in pointed protomodular categories

Martins-Ferreira, N.

http://hdl.handle.net/10400.8/15068

Use this identifier to reference this record.

Name:	Description:	Size:	Format:
Star-multiplicative graphs in pointed protomodular categories.pdf	Protomodularity, in the pointed case, is equivalent to the Split Short Five Lemma. It is also well known that this condition implies that every internal category is in fact an internal groupoid. In this work, this is condition (II) and we introduce two other conditions denoted (I) and (III). Under condition (I), every multiplicative graph is an internal category. Under condition (III), every star-multiplicative graph can be extended (uniquely) to a multiplicative graph, a problem raised by G. Janelidze in [10] in the semiabelian context. When the three conditions hold, internal groupoids have a simple description, that, in the semiabelian context, correspond to the notion of internal crossed module, in the sense of [10].	281.95 KB	Adobe PDF	Download

Send Feedback

Authors

Martins-Ferreira, N.

Abstract(s)

Protomodularity, in the pointed case, is equivalent to the Split Short Five Lemma. It is also well known that this condition implies that every internal category is in fact an internal groupoid. In this work, this is condition (II) and we introduce two other conditions denoted (I) and (III). Under condition (I), every multiplicative graph is an internal category. Under condition (III), every star-multiplicative graph can be extended (uniquely) to a multiplicative graph, a problem raised by G. Janelidze in [10] in the semiabelian context. When the three conditions hold, internal groupoids have a simple description, that, in the semiabelian context, correspond to the notion of internal crossed module, in the sense of [10].

Description

Fonte: http://www.tac.mta.ca/tac/volumes/23/9/23-09.pdf

Keywords

Internal category internal groupoid re°exive graph multiplicative graph star-multiplicative graph jointly epic pair admissible pair jointly epic split extension split short ¯ve lemma pointed protomodular

URI

http://hdl.handle.net/10400.8/15068

Citation

Martins-Ferreira, N. (2010). Star-multiplicative graphs in pointed protomodular categories. Theory and Applications of Categories, 23(9), 170-198. DOI: https://doi.org/10.70930/tac/iodb71v5.